Sounds like you have electrical gremlins. The starter relay has a fuse, and lots of wires to check. Get a good diagram, see page 386 of the Ford, Lincoln and Mercury Service Manual, 1942-1948. You can get a reprinted manual from the resources page or on the web, try e-bay. When the OD solenoid drops out, the engine is disconnected from the rear wheels, and the signal light goes out. Check connections to relay, solenoid, kick-down switch, and governor. Could be an intermittent in any of these places.
Abe